What is the definition of a rank 3 totally antisymmetric tensor?

[ehrenfest]

Homework Statement

The totally antisymmetric rank 4 tensor is defined as 1 for an even combination of its indices and -1 for an odd combination of its indices and 0 otherwise.

Is a rank 3 totally antisymmetric tensor defined the same way?

Homework Equations

The Attempt at a Solution

 

[Dick]

Mmmmmm. Yes! Do you think 4 is special?

 

[George Jones]

The definition is the same, but remember that a cyclic permuation is even/odd iff the number of elements being permuted is odd/even. This sometimes causes confusion when moving moving from 3 to 4 dimensions.

 

[jeckster]

Mmmmmm. Yes! Do you think 4 is special?

Could you please answer this question:
link: https://www.physicsforums.com/showthread.php?t=466675

thanks a lot

 

[pvukovic]

Yes and no, I think the definition here is incomplete. It does not include what happens when you raise and lower an index. The rank 4 anti-symmetric tensor is a psuedotensor, the rank 3 one is a true tensor. So overall no.